11.2 Particle conservation laws

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By the end of this section, you will be able to:
• Distinguish three conservation laws: baryon number, lepton number, and strangeness
• Use rules to determine the total baryon number, lepton number, and strangeness of particles before and after a reaction
• Use baryon number, lepton number, and strangeness conservation to determine if particle reactions or decays occur

Conservation laws are critical to an understanding of particle physics. Strong evidence exists that energy, momentum, and angular momentum are all conserved in all particle interactions. The annihilation of an electron and positron at rest, for example, cannot produce just one photon because this violates the conservation of linear momentum. As discussed in Relativity , the special theory of relativity modifies definitions of momentum, energy, and other familiar quantities. In particular, the relativistic momentum of a particle differs from its classical momentum by a factor $\gamma =1\text{/}\sqrt{1-{\left(v\text{/}c\right)}^{2}}$ that varies from 1 to $\infty ,$ depending on the speed of the particle.

In previous chapters, we encountered other conservation laws as well. For example, charge is conserved in all electrostatic phenomena. Charge lost in one place is gained in another because charge is carried by particles. No known physical processes violate charge conservation. In the next section, we describe three less-familiar conservation laws: baryon number, lepton number, and strangeness. These are by no means the only conservation laws in particle physics.

Baryon number conservation

No conservation law considered thus far prevents a neutron from decaying via a reaction such as

$\text{n}\to {\text{e}}^{+}+{\text{e}}^{\text{−}}.$

This process conserves charge, energy, and momentum. However, it does not occur because it violates the law of baryon number conservation. This law requires that the total baryon number of a reaction is the same before and after the reaction occurs. To determine the total baryon number, every elementary particle is assigned a baryon number     B . The baryon number has the value $B=+1$ for baryons, –1 for antibaryons, and 0 for all other particles. Returning to the above case (the decay of the neutron into an electron-positron pair), the neutron has a value $B=+1,$ whereas the electron and the positron each has a value of 0. Thus, the decay does not occur because the total baryon number changes from 1 to 0. However, the proton-antiproton collision process

$\text{p}+\stackrel{\text{−}}{\text{p}}\to \text{p}+\text{p}+\stackrel{\text{−}}{\text{p}}+\stackrel{\text{−}}{\text{p}},$

does satisfy the law of conservation of baryon number because the baryon number is zero before and after the interaction. The baryon number for several common particles is given in [link] .

Conserved properties of particles
Particle name Symbol Lepton number $\left({L}_{e}\right)$ Lepton number $\left({L}_{\mu }\right)$ Lepton number $\left({L}_{\tau }\right)$ Baryon number ( B ) Strange-ness number
Electron ${\text{e}}^{\text{−}}$ 1 0 0 0 0
Electron neutrino ${\upsilon }_{e}$ 1 0 0 0 0
Muon ${\mu }^{\text{−}}$ 0 1 0 0 0
Muon neutrino ${\upsilon }_{\mu }$ 0 1 0 0 0
Tau ${\tau }^{\text{−}}$ 0 0 1 0 0
Tau neutrino ${\upsilon }_{\tau }$ 0 0 1 0 0
Pion ${\pi }^{+}$ 0 0 0 0 0
Positive kaon ${\text{K}}^{+}$ 0 0 0 0 1
Negative kaon ${\text{K}}^{\text{−}}$ 0 0 0 0 –1
Proton p 0 0 0 1 0
Neutron n 0 0 0 1 0
Lambda zero ${\text{Λ}}^{0}$ 0 0 0 1 –1
Positive sigma ${\text{Σ}}^{+}$ 0 0 0 1 –1
Negative sigma ${\text{Σ}}^{\text{−}}$ 0 0 0 1 –1
Xi zero ${\text{Ξ}}^{0}$ 0 0 0 1 –2
Negative xi ${\text{Ξ}}^{\text{−}}$ 0 0 0 1 –2
Omega ${\text{Ω}}^{\text{−}}$ 0 0 0 1 –3

Baryon number conservation

Based on the law of conservation of baryon number, which of the following reactions can occur?

$\begin{array}{}\\ \\ \left(\text{a}\right)\phantom{\rule{0.2em}{0ex}}{\pi }^{\text{−}}+\text{p}\to {\pi }^{0}+\text{n}+{\pi }^{\text{−}}+{\pi }^{+}\hfill \\ \left(\text{b}\right)\phantom{\rule{0.2em}{0ex}}\text{p}+\stackrel{\text{−}}{\text{p}}\to \text{p}+\text{p}+\stackrel{\text{−}}{\text{p}}\hfill \end{array}$

Strategy

Determine the total baryon number for the reactants and products, and require that this value does not change in the reaction. Solution

For reaction (a), the net baryon number of the two reactants is $0+1=1$ and the net baryon number of the four products is $0+1+0+0=1.$ Since the net baryon numbers of the reactants and products are equal, this reaction is allowed on the basis of the baryon number conservation law.

For reaction (b), the net baryon number of the reactants is $1+\left(-1\right)=0$ and the net baryon number of the proposed products is $1+1+\left(-1\right)=1.$ Since the net baryon numbers of the reactants and proposed products are not equal, this reaction cannot occur.

Significance

Baryon number is conserved in the first reaction, but not in the second. Baryon number conservation constrains what reactions can and cannot occur in nature.

Questions & Answers

as a free falling object increases speed what is happening to the acceleration
Success Reply
of course g is constant
Alwielland
acceleration also inc
Usman
photo electrons doesn't emmit when electrons are free to move on surface of metal why?
Rafi Reply
What would be the minimum work function of a metal have to be for visible light(400-700)nm to ejected photoelectrons?
Mohammed Reply
give any fix value to wave length
Rafi
40 cm into change mm
Arhaan Reply
40cm=40.0×10^-2m =400.0×10^-3m =400mm. that cap(^) I have used above is to the power.
Prema
i.e. 10to the power -2 in the first line and 10 to the power -3 in the the second line.
Prema
there is mistake in my first msg correction is 40cm=40.0×10^-2m =400.0×10^-3m =400mm. sorry for the mistake friends.
Prema
40cm=40.0×10^-2m =400.0×10^-3m =400mm.
Prema
this msg is out of mistake. sorry friends​.
Prema
what is physics?
sisay Reply
why we have physics
Anil Reply
because is the study of mater and natural world
John
because physics is nature. it explains the laws of nature. some laws already discovered. some laws yet to be discovered.
Yoblaze
is this a physics forum
Physics Reply
explain l-s coupling
Depk Reply
how can we say dirac equation is also called a relativistic equation in one word
preeti Reply
what is the electronic configration of Al
usman Reply
what's the signeficance of dirac equetion.?
Sibghat Reply
what is the effect of heat on refractive index
Nepal Reply
As refractive index depend on other factors also but if we supply heat on any system or media its refractive index decrease. i.e. it is inversely proportional to the heat.
ganesh
you are correct
Priyojit
law of multiple
Wahid
if we heated the ice then the refractive index be change from natural water
Nepal
can someone explain normalization condition
Priyojit Reply
please tell
Swati
yes
Chemist
1 millimeter is How many metres
Darling Reply
1millimeter =0.001metre
Gitanjali
The photoelectric effect is the emission of electrons when light shines on a material.
Chris Reply

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 By By Anindyo Mukhopadhyay